# Deep Gaussian Process Emulation using Stochastic Imputation

arXiv: https://arxiv.org/abs/2107.01590 · HTML: https://mlsanity.com/paper/2107.01590/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 51 references that are in the map.
- First posted on arXiv 4 Jul 2021.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Deep Gaussian Processes for Regression using Approximate Expectation Propagation](https://mlsanity.com/paper/1602.04133/) (2016)
- [Active Learning for Deep Gaussian Process Surrogates](https://mlsanity.com/paper/2012.08015/) (2020)
- [Avoiding pathologies in very deep networks](https://mlsanity.com/paper/1402.5836/) (2014)
- [Inference in Deep Gaussian Processes using Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1806.05490/) (2018)
- [Bayesian Optimization using Deep Gaussian Processes](https://mlsanity.com/paper/1905.03350/) (2019)
- [GPflux: A Library for Deep Gaussian Processes](https://mlsanity.com/paper/2104.05674/) (2021)
- [Computer emulation with non-stationary Gaussian processes](https://mlsanity.com/paper/1308.4756/) (2013)
- [Diagnostic-Driven Nonstationary Emulators Using Kernel Mixtures](https://mlsanity.com/paper/1803.04906/) (2018)

## Built on by (most cited first, 11 of 11)

- [SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes](https://mlsanity.com/paper/2305.13998/) (2023)
- [A mixed-categorical correlation kernel for Gaussian process](https://mlsanity.com/paper/2211.08262/) (2022)
- [Statistical Deep Learning for Spatial and Spatio-Temporal Data](https://mlsanity.com/paper/2206.02218/) (2022)
- [Collaborative and Distributed Bayesian Optimization via Consensus: Showcasing the Power of Collaboration for Optimal Design](https://mlsanity.com/paper/2306.14348/) (2023)
- [High-dimensional mixed-categorical Gaussian processes with application to multidisciplinary design optimization for a green aircraft](https://mlsanity.com/paper/2311.06130/) (2023)
- [Multi-Agent Reinforcement Learning Simulation for Environmental Policy Synthesis](https://mlsanity.com/paper/2504.12777/) (2025)
- [Linked Deep Gaussian Process Emulation for Model Networks](https://mlsanity.com/paper/2306.01212/) (2023)
- [On the meaning of uncertainty for ethical AI: philosophy and practice](https://mlsanity.com/paper/2309.05529/) (2023)
- [Integrative Analysis and Imputation of Multiple Data Streams via Deep Gaussian Processes](https://mlsanity.com/paper/2505.12076/) (2025)
- [Deep Intrinsic Coregionalization Multi-Output Gaussian Process Surrogate with Active Learning](https://mlsanity.com/paper/2508.16434/) (2025)
- [Actively Learning Joint Contours of Multiple Computer Experiments](https://mlsanity.com/paper/2512.13530/) (2025)

## Abstract (arXiv)

Deep Gaussian processes (DGPs) provide a rich class of models that can better represent functions with varying regimes or sharp changes, compared to conventional GPs. In this work, we propose a novel inference method for DGPs for computer model emulation. By stochastically imputing the latent layers, our approach transforms a DGP into a linked GP: a novel emulator developed for systems of linked computer models. This transformation permits an efficient DGP training procedure that only involves optimizations of conventional GPs. In addition, predictions from DGP emulators can be made in a fast and analytically tractable manner by naturally utilizing the closed form predictive means and variances of linked GP emulators. We demonstrate the method in a series of synthetic examples and empirical applications, and show that it is a competitive candidate for DGP surrogate inference, combining efficiency that is comparable to doubly stochastic variational inference and uncertainty quantification that is comparable to the fully-Bayesian approach. A textttPython package textttdgpsi implementing the method is also produced and available at https://github.com/mingdeyu/DGP.